Hi,
In this question, we are given information in terms of cubic meters and kilograms, and asked for an answer in terms of cubic centimeters and grams.
The proportion that the question tells us is:
1 cubic meter/800 kilograms = x cubic centimeters/1 gram
We will need to convert kilograms to grams, and cubic meters to cubic centimeters. We will first convert the left side to cubic centimeters and grams, then solve for x.
We are told that 1 kilogram = 1000 grams and 1 cubic meter = 1,000,000 cubic centimeters.
To convert units, we must multiply by quantities that are equal to 1, so that we do not alter the fundamental value. In this case, we can multiply by 1 kilogram/1000 grams or 1000 grams/1 kilogram, because these fractions are both equal to 1. That is, 1000 grams = 1 kilogram.
To convert 1 cubic meter to cubic centimeters, multiply by 1,000,000 cubic centimeters/1 cubic meter. It is important to put 1 cubic meter in the denominator of the fraction, so that the cubic meter terms cancel out and we are left with cubic centimeters.
1 cubic meter * 1,000,000 cubic centimeters/1 cubic meter = 1,000,000 cubic centimeters.
Similarly,
800 kilograms * 1000 grams/1 kilogram = 800,000 grams.
So, 1 cubic meter/800 kilograms = 1,000,000 cubic centimeters/800,000 grams. This reduces to 1.25 cubic centimeters/1 gram.
Since we are looking for x in the expression (x cubic centimeters/1 gram), the answer is 1.25.
